d = 1/I0- e expectation of life goes up by one third as much for a small improve-t in the rate at age 55 as it does for the same size of improvement at age len the death rate goes down by about one third as much. Thus on the 3nary model it makes three times as much difference for the overall i rate to have an improvement at age 0 as to have the same improvement \Q 55. It also makes three times as much difference to the number of )ns living at any moment per 1,000 births. owever, in real life deaths and births are not equal, and we can make our 3! more realistic, at least to the extent of recognizing this inequality. For icreasing population, the above result becomes even stronger. Moreover, ivolving birth as well as death we will find that the more important result 1 improvement in infant mortality (as against an improvement at ages 55 9) is through its impact on the birth rate. We proceed to the study of ilation replacement through birth and death. '.lation Replacement per Generation he population process seen as the replacement of one generation by her is conveniently summarized by the Net Reproduction Rate,.R0. This 2 expected number of girl children to which a girl child now bom will in give birth, the expectation typically based on the age-specific rates of . and death in a given year or other period. In the continuous one-sex R0 = f p(a)m(a)da, a •e p(a) is the probability of surviving from age 0 to age a, m(a)da the ce of having a girl child between ages a and a + da, a and 0 the lowest highest ages of possible reproduction. In terms of the observations in ir age intervals, •Q 5LX is the number of women reaching ages x to x + 4 at last birth-out of 1Q births, and Fx is the age-specific birth rate to women aged x + 4 at last birthday. (The need to use two sets of symbols and to uce two formulas arises because theoretical propositions are often ex-ed and derived in the continuous form, but that form has to be0 years ago, when the fall in mortality greatly increased the rate of growth and tended to make the population much younger.